Lab 3: Force, Mass, and Acceleration
39
Name_________________________ Section_______ Date_____________
Pre-Lab Preparation Sheet for Lab 3:
Force, Mass, and Acceleration
(Due at the Beginning of Lab)
Directions:
Read over the lab and then answer the following questions.
1. Consider the experimental configuration shown in Figure 1. Starting from Newton’s 2nd
law, show that the acceleration of the cart is on the string is given by:
mg
.
a=
m+M
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 118A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
40
Lab 3: Force, Mass, and Acceleration
2. In the limit where M >> m, what is the tension T in the string?
3. In the limit where M << m, what is the tension T in the string?
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 114A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
Lab 3: Force, Mass, and Acceleration
41
Name _____________________ Date __________
TA
________________
Partners ________________
Section _______
________________
Lab 3: Force, Mass, and Acceleration
“Well, the Force is what gives a Jedi his power . . . . It surrounds us
and penetrates us. It binds the galaxy together.”
-- Obi-Wan Kenobi on Newton’s 2nd Law
Equipment
Motion sensor
Force sensor
Low-friction cart
2.2 meter track
Torpedo level
Low –friction pulley
Foam crash pad
0.02, 0.05, 0.10, and 0.20 kg hooked mass
Note: The acceleration due to gravity varies with location. Here at Vanderbilt,
the is
g = ( 9.7943 ± 0.0032 )
m
s2
Use this value throughout the semester.
Introduction
Newton’s 2nd Law:
Fnet = ma
If you know the mass and net force on an object, you know the acceleration of the object.
If you know the acceleration of an object and its initial velocity and its initial position, you know the
complete trajectory of the object.
Consider the problem illustrated below: a frictionless wheeled cart is pulled by string attached to a falling
mass.
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 118A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
42
Lab 3: Force, Mass, and Acceleration
M
pulley
m
Fig. 1
It can be shown that the acceleration a is given by
a=
mg
M +m
(1)
Of course, that is the theory. In the real world, things can get messy. Welcome to experimental physics.
Exercise 1: Data Acquisition
1. Label the individual forces on the diagram above.
2. Mass the combined cart and force sensor with the electronic scale
M = _______________________________________
Note: Before each measurement with the scale, you should tare the
scale. Empty the scale, then press the Z or TARE button found on the
panel. This resets the zero point of the scale.
You will be using a set of hooked weights for you falling masses. These have nominal values of 0.020 kg,
0.050 kg, 0.100 kg, 0.200 kg.
3. Measure their precise masses with the digital scale and record the results and associated
uncertainties on Table 1 below.
You will use the PASCO Force Sensor to measure the tension in the string. Note the sign convention for
the direction of the force on the hook.
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 114A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
Lab 3: Force, Mass, and Acceleration
43
Assemble the cart, force sensor, string, and falling mass. The falling mass will be one of four hooked
weights: 0.020 kg, 0.050 kg, 0.100 kg, 0.200 kg. Verify that a crash pad is positioned underneath the
falling mass.
4. Run the Capstone program Velocity&Force.
Note: Before each measurement with the force sensor, you must tare
the force sensor. Remove any force from the hook, then press the TARE
button found on the side of the sensor. This will ensure that when the
force is zero, the device returns zero.
5. Holding cart stationary, measure the static tension Tstatic on the string and the
corresponding uncertainty. Record the result in Table 1 below. Briefly explain how you
determined the uncertainty below.
Note: Do not assume that every digit which Capstone reports is significant!
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 118A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
44
Lab 3: Force, Mass, and Acceleration
Table 1: Measured values
m
Tstatic
Tdynamic
a
6. Dedicate one of you members to catching the cart before it crashes into the pulley.
Please, do not turn this into a projectile motion lab!
7. Start recording, then release the cart. Record the dynamic tension on the string Tdynamic,
the acceleration a, and the associated uncertainties. Justify your determination of each of
these uncertainties below.
Exercise 2: Data Analysis
8. In the pre-lab, you calculated the dynamic tension in the limit of m << M. Is this
confirmed in your observations? Using Excel, plot your data in way to support your
argument.
While you have measured the acceleration above, it can also be calculated from Equ. 1, or from the
measured tension of the string and the cart mass.
9. Fill in the table below. Include the associated uncertainties
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 114A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
Lab 3: Force, Mass, and Acceleration
45
Table 2: Calculated accelerations
mg
M +m
Tdynamic
M
10. Are the measurements in Table 2 consistent with each other? Explain.
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 118A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
46
Lab 3: Force, Mass, and Acceleration
11. Are the measurements of
Tdynamic
M
consistent with the measured accelerations a in Table 1?
Explain.
12. Thus far, we have been blithely ignoring friction of the cart. Given that friction is present,
how would that effect the acceleration of the cart and the tension of the string?
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 114A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton
Lab 3: Force, Mass, and Acceleration
47
13. Would the addition of a constant friction force resolve any discrepancy between the
observed acceleration and the observed dynamic tension? Explain.
Vanderbilt University, Dept. of Physics & Astronomy
PHYS 118A
Modified from: RealTime Physics, P. Laws, D. Sokoloff, R. Thornton
and University of VA Physics Labs: S. Thornton